Construct a parallelogram ABCD, in which diagonal AC = 3.8 cm,

 We know that the diagonals of a parallelogram bisect each other.

Steps of construction:

Step 1: Draw $A C=3.8 \mathrm{~cm}$

Step 2: Bisect $A C$ at $O$.

Step 3: Make $\angle C O X=60^{\circ}$

Produce $X O$ to $Y$.

Step 4:

$O B=\frac{1}{2}(4.6) \mathrm{cm}$ $O B=2.3 \mathrm{~cm}$ and $O D=\frac{1}{2}(4.6) \mathrm{cm}$ $O D=2.3 \mathrm{~cm}$

Sten 5. Join $A B, B C, C D$ and $A D$

​Thus, ABCD is the required parallelogram.